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Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds

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Abstract

This paper contains some vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds with a weighted Poincaré inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but without assumptions of sign and growth rate of the weight function, so they can be applied to complete stable hypersurfaces.

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  1. Departamento de Matemática, Universidade Federal do Espírito Santo, Vitória, 29075-910, Brazil

    Matheus Vieira

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  1. Matheus Vieira
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Vieira, M. Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds. Geom Dedicata 184, 175–191 (2016). https://doi.org/10.1007/s10711-016-0165-1

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  • DOI: https://doi.org/10.1007/s10711-016-0165-1

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